3L 4s - "mosh"

MOS scales of this form are built from a generator that falls between 1\3 (one degree of 3edo - 400 cents) and 2\7 (two degrees of 7edo - 343 cents.

It has the form s L s L s L s and its various "modes" (with Modal UDP Notation and nicknames coined by Andrew Heathwaite) are:

Mode	UDP	Nickname
s L s L s L s	3|3	bish
L s L s L s s	6|0	dril
s L s L s s L	2|4	fish
L s L s s L s	5|1	gil
s L s s L s L	1|5	jwl
L s s L s L s	4|2	kleeth
s s L s L s L	0|6	led

The two notable harmonic entropy minima with this pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and magic, where the generator is a 5/4 but five of them make a 3/1.

			g	2g	3g	4g (-1200)	comments
1\3			400.000	800.000	1200.000	400.000
	15\46		391.304	782.609	1173.913	365.217
	14\43		390.698	781.395	1172.093	362.791
	13\40		390.000	780.000	1170.000	360.000
	12\37		389.189	778.378	1167.568	356.757
	11\34		388.235	776.471	1164.706	352.941
	10\31		387.097	774.194	1161.290	348.387	Würschmidt is around here
		19\59	386.441	772.881	1159.322	345.763
	9\28		385.714	771.429	1157.143	342.857
	8\25		384.000	768.000	1152.000	336.000
		23\72	383.333	766.667	1150.000	333.333
		15\47	382.988	765.957	1148.936	331.915
	7\22		381.818	763.636	1145.455	327.273
		13\41	380.488	760.976	1141.463	321.951	Magic is around here
		19\60	380.000	760.000	1140.000	320.000
		25\79	379.747	759.494	1139.2405	318.987
	6\19		378.947	757.895	1136.842	315.789
		11\35	377.143	754.286	1131.429	308.571
		16\51	376.471	752.941	1129.412	305.882
	5\16		375.000	750.000	1125.000	300.000	L/s = 4
		24\77	374.026	748.052	1122.078	296.104
		19\61	373.7705	747.541	1121.3115	295.082
		14\45	373.333	746.667	1120.000	293.333
		9\29	372.414	744.828	1117.241	289.655
		13\42	371.429	742.857	1114.286	285.714
		17\55	370.909	741.818	1112.727	283.636
			370.204	740.409	1110.613	280.817	L/s = pi
	4\13		369.231	738.462	1107.692	276.923	L/s = 3
		23\75	368.000	736.000	1104.000	272.000
		19\62	367.742	735.484	1103.226	270.968
		15\49	367.347	734.694	1102.041	269.388
			367.091	734.183	1101.274	268.365	L/s = e
		11\36	366.667	733.333	1100.000	266.667
			366.256	732.513	1198.77	265.026
		7\23	365.217	730.435	1095.652	260.870	Modi Sephiratorum (Kosmorsky)
		17\56	364.286	728.571	1092.857	257.143
		10\33	363.636	727.272	1090.909	254.545
		13\43	362.791	725.581	1088.372	251.163
		16\53	362.264	724.528	1086.7925	249.057
		19\63	361.905	723.8095	1085.714	247.619
	3\10		360.000	720.000	1080.000	240.000	Boundary of propriety(generators smaller than this are proper)
		38\127	359.055	718.110	1077.165	236.2205
		35\117	358.974	717.949	1076.923	235.898
		32\107	358.8785	717.757	1076.6355	235.514
		29\97	358.763	717.526	1076.289	235.0515
		26\87	358.621	717.241	1075.862	234.483
		23\77	358.442	716.883	1075.325	233.767
		20\67	358.209	716.418	1074.627	232.836
		17\57	357.895	715.7895	1073.684	231.579
		14\47	357.447	714.894	1072.340	229.787
		11\37	356.757	713.514	1070.270	227.027
			356.5035	713.007	1069.511	226.014
		8\27	355.556	711.111	1066.667	222.222	Beatles is around here
			354.930	709.859	1064.789	219.718	Golden neutral thirds scale
		21\71	354.783	709.565	1064.348	219.13
		13\44	354.5455	709.091	1063.636	218.182
			354.088	708.177	1062.266	216.354
	5\17		352.941	705.882	1058.824	211.765	Optimum rank range (L/s=3/2)
		12\41	351.220	702.439	1053.659	204.878	2.3.11 neutral thirds scale is around here
	7\24		350.000	700.000	1050.000	200.000
		16\55	349.091	698.182	1047.273	196.364
	9\31		348.387	696.774	1045.161	193.548	Mohajira/dicot is around here
	11\38		347.368	694.737	1042.105	189.474
2\7			342.857	685.714	1028.571	171.429

3\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. 17edo neutral scale), and something else I don't have a name for yet on the top, with 10edo standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS 7L 3s ("unfair mosh"); the other scales make MOS 3L 7s ("fair mosh").

In "neutral third scale territory," the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone".

In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a "supermajor second" to a "major third" and s is a "semitone" or smaller.